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Homomorphisms Between Lattices of Zero-Sets

Published online by Cambridge University Press:  20 November 2018

S. Broverman
S. Broverman*
Affiliation:
Mathematics Department, University Of Toronto, Toronto Ont.
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Abstract

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For a completely regular Hausdorff topological space X, let Z(X) denote the lattice of zero-sets of X. If T is a continuous map from X to Y, then there is a lattice homomorphism T” from Z(Y) to Z(X) induced by T which is defined by τ‘(A) = τ←(A). A characterization is given of those lattice homomorphisms from Z(Y) to Z(X) which are induced in the above way by a continuous function from X to Y.

Keywords

54C0554C5054D3554D60zero-set latticelattice homomorphismz-ultrafilterrealcompactStone-Cech compactification
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 1 , 01 March 1978 , pp. 1 - 5
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Gillman, L. and Jerison, M., Rings of continuous functions, Van Nostrand, Princeton, 1960.Google Scholar
2. Mandelker, Mark, F-spaces and z-embedded subspaces, Pacific J. of Math. 28 (1969), 615-621.Google Scholar
3. Stone, M. H., Applications of the theory of Boolean rings to general topology, Trans, Amer. Math. Soc. 41 (1937), 375-481.Google Scholar